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Real Backgammon

Posted By: Maik Stiebler
Date: Friday, 30 April 2010, at 10:45 a.m.

In Response To: Real Backgammon (Daniel Murphy)

I think there is no definitive answer to the question without further restrictions. If we assume that it's actually a DMP session, and the -0.100 error appears randomly in one of the matches, the spectacular solution seems to be that the blundering opponent will be ahead with a probability of 37.6895%, and behind with a probability of 37.6888%.

Without the DMP assumption, the result depends on the exact distribution of results with and without blundering, which I guess is part of what Timothy is saying.

Even with the DMP assumption, the answer will depend on whether you or opponent can choose a particular moment for the blunder to appear. For example, let's say it's game 9, and opponent, who hasn't blundered yet, is leading 5-3 and 100% to win the ninth game if he plays correctly. Now he has the choice of blundering now, reducing MWC to 95% in game 9 but starting at 50.5% in game 10, or blundering in game 10, making it 45.5% for that game. Obviously the second choice is better for the opponent in the sense that it ensures a session win, although equitywise they are the same.

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